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Chapter 7: Q 80. (page 453)

Shortest Distance from Honolulu to Melbourne, Australia: Find the shortest distance from Honolulu to Melbourne, Australia, latitude 37掳47 S, longitude 144掳58E. Round your answer to the nearest mile.

Short Answer

Expert verified

The distance 5625 miles.

Step by step solution

01

Step 1. Given information.

Consider the given angles as:

伪1,尾1=lat,lon=37掳47,144掳58

02

Step 2. Find the nearest distance.

Since the only one point value is given. Let's take another point value as zero. The radius is 3960 miles.

伪2,尾2=0,0

Substitute all the values in the given formula,

d=rcos-1cos伪1cos尾1cos伪2cos尾2+cos伪1sin尾1cos伪2sin尾2+sin伪1sin伪2=3960cos-1cos37掳47cos144掳58cos0cos0+cos37掳47sin144掳58cos0sin0+sin37掳47sin0=3960cos-1cos37掳47cos144掳581+0+0=3960cos-10.484800.30901=3960cos-10.149808048鈮�5625miles

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